Digital technologies keep track of everything we do and say while we are online, and we spend online an increasing portion of our time. Databases hidden behind web services and applications are constantly fed with information of our movements and communication patterns, and a significant dimension of our lives, quantified to unprecedented levels, gets stored in those vast online repositories. This article considers some of the implications of this torrent of data for social science research, and for the types of questions we can ask of the world we inhabit. The goal of the article is twofold: to explain why, in spite of all the data, theory still matters to build credible stories of what the data reveal; and to show how this allows social scientists to revisit old questions at the intersection of new technologies and disciplinary approaches. The article also considers how Big Data research can transform policymaking, with a focus on how it can help us improve communication and governance in policy-relevant domains.